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Journals ACM Communications in Computer Algebra Volume 40 Issue 2

In differential algebra 1, rankings on partial derivatives play the same role as admissible term orders in the theory of Gröbner bases. In fact, an admissible term order is a particular case of a ranking on partial derivatives of a single differential indeterminate. The introduction of a ranking allows to select leading derivatives in differential polynomials, define a pseudo-reduction relation, and consider autoreduced sets; the latter are the a tool for representing differential ideals.

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Construction of rankings on partial derivatives

Golubitsky, Oleg
ACM Communications in Computer Algebra , Volume 40 (2)
Association for Computing Machinery – Jun 1, 2006

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